The Appell function in (REF ) matches the reduction
formula (see Eq. (1) in section 5.10 in Ref. [1]});
\(F_1(a,b_1,b_2,b_1+b_2,x,y)=(1-y)^{-a}\,\phantom{}_2F_1\left(a,b_1,b_1+b_2,\frac{x-y}{1-y}\right)\,.\) 
